求解BBM方程的一个两层线性化差分格式

本文对一类带有齐次边界条件的Benjamin-Bona-Mahony方程(BBM方程)的初边值问题进行了数值研究,提出了一个具有二阶理论精度的两层线性化差分格式,该格式合理地模拟了原问题的一个守恒性质.本文证明了该格式差分解的存在唯一性.综合运用数学归纳法和离散泛函分析方法,本文还证明了该差分格式的收敛性和稳定性.数值实验表明该方法是可靠的.

A linear two-level difference scheme for solving BBM equation

In this paper, the numerical solution of initial-boundary value problem for Benjamin-Bona-Mahony equation with homogeneous boundary is considered. A two-level linearized difference scheme with the second order is proposed. The difference scheme simulates the conservation property of the problem quite well. Then the existence and uniqueness of the difference solutions are also proved. In the case that the maximum mold estimator of the difference solutions cannot be obtained, it is proved that the difference scheme is convergent and stable by mathematical induction and the discrete function analysis.And the results are demonstrated by the numerical examples.